FISHERY BULLETIN: VOL. 84, NO. 2 



previous quarter (i.e., the same nominal effort was 

 applied to a smaller population). The result was that 

 yield was overestimated for April-June and under- 

 estimated for July-September, but estimated reason- 

 ably accurately for the season. 



We attempted to simulate reality by using multi- 

 ples of the fishing mortality distribution that we 

 observed in the 1964-77 data base. Fishing mortal- 

 ity imposed to mimic current conditions was ob- 

 tained by taking the mean fishing mortality at age 

 by quarter from the cohort analysis conducted on 

 the 1960-76 year classes (1964-77 fishing years). The 

 mean mortality on ages 2-4 fish was used, along with 

 a mortality obtained from a scaling factor of 0.362 

 for age 1 (Table 10). Input population size to start 

 the simulation runs was the mean population num- 

 ber-at-age as of 1 January, the arbitrarily assigned 

 birth date of gulf menhaden. Those numbers were 

 16,030 million, 2,813 million, 227.9 million, and 

 10.78 million for ages 1-4. The model was run over 

 a range from to 2.75 times the average fishing 

 mortality and was also used to iterate to MSY under 

 the current distribution of fishing mortality by age 

 (Table 10). 



The overall catch-effort curve from multiple runs 

 indicates that the fishery is operating slightly before 

 the MSY level (Fig. 9, Table 10). At the currents- 

 multiple of 1.0, the fishery should sustain an average 

 yield of about 565,581 t, assuming no variance in 

 recruitment from the hypothetical spawner-recruit 

 curve. 



The model predicts a MSY of about 585,118 t at 

 127% of the average fishing mortality for the 

 1964-77 fishing seasons. We feel that this model, 



which incorporates a spawner-recruit relationship 

 and recruitment pattern plus growth and natural 

 mortality rates, provides a better estimate of long- 

 term MSY than does a model based on a simple 

 catch-effort production function. Considerable fluc- 

 tuation in yield will result from fluctuations in 

 recruitment, but the long-term MSY estimate 

 appears to be realistic, provided that the esti- 

 mated spawner-recruit relationship is valid and 

 that the basic pattern of recruitment remains 

 unchanged. 



The Walters' model also identifies the level of 

 fishing mortality at which the population is no longer 

 sustainable, i.e., a biological break-even point. The 

 extinction point occurs at an F- multiple of 2.50 

 (150% greater than current fishing mortality), al- 

 though the model indicates that such extinction 

 would involve a gradual decline over a period of 

 many years, again assuming that "average" condi- 

 tions prevailed (Fig. 9). Increasing the fishing mor- 

 tality beyond an F-multiple of 2.50 results in a more 

 rapid rate of extinction (Table 10). 



Results of low and high F-multiple levels show 

 steep slopes on the ascending and descending limbs 

 of the production function curve (Fig. 9). The 

 ascending limb behaves similarly to the curves in 

 the yield-per-recruit model as fishing mortality rates 

 go from low to current levels (Fig. 7). At mortality 

 rates higher than current levels, however, the yield- 

 per-recruit model cannot be used to evaluate poten- 

 tial yield because of the impact of heavy fishing 

 mortality on the spawning stock and the subsequent 

 reduction in recruitment. For example, under the 

 average recruitment level of 16.03 billion fish at age 



Table 10. — Annual age-specific fishing mortality rates for gulf menhaden, ex- 

 pressed as multiples of the average fishing mortality rate at age, 1964-77, (F- 

 multiple = 1.00), actual fishing mortality rates at age used in the population 

 simulation model, sustainable yield, population biomass, and years to 

 stabilization. 



1 To extinction. 



322 



